An angle with its vertex at the center of a circle intercepts an 80° arc of that circle.
What is the measure of the angle?
Answers
let's recall that, arc's angle measures come from the central angle they're in.
if this intercepted arc is 80°, and is intercepted by an angle stemming from the center, namely a central angle, then the angle is also 80°. Check the picture below.
If angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is 80°.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that angle with its vertex at the center of a circle intercepts an 80° arc of that circle
We have to find the measure of the angle.
When an angle is formed at the center of a circle, it intercepts an arc of the circle that is equal in measure to the angle.
Since the given angle intercepts an 80° arc of the circle, we know that its measure is also 80°. so the measure of the angle is 80°.
Hence, if angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is 80°.
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ2
Related Questions
Determine the domain of the function f (x) = 2x - 4 when the range is (0, 12, 20)
Answers
Answer:
The domain is (2,8,12)
Step-by-step explanation:
we have
[tex]f(x)=2x-4[/tex]
we know that
The range is (0,12,20)
Find the domain
1) For f(x)=0 -----> Find the value of x
substitute the value of f(x) in the equation and solve for x
[tex]0=2x-4[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
therefore
For f(x)=0 the domain is x=2
2) For f(x)=12 -----> Find the value of x
substitute the value of f(x) in the equation and solve for x
[tex]12=2x-4[/tex]
[tex]2x=12+4[/tex]
[tex]x=8[/tex]
therefore
For f(x)=12 the domain is x=8
3) For f(x)=20 -----> Find the value of x
substitute the value of f(x) in the equation and solve for x
[tex]20=2x-4[/tex]
[tex]2x=20+4[/tex]
[tex]x=12[/tex]
therefore
For f(x)=20 the domain is x=12
therefore
The domain is (2,8,12)
Simplify: |3 – 10| - (12 / 4 + 2)^2
Answers
Answer:
-18
Step-by-step explanation:
= |3 – 10| - (12 / 4 + 2)^2
= 7 - (3 + 2)^2
= 7 - (5)^2
= 7 - 25
= -18
Triangles are congruent if they have the same ____.
Answers
Answer:
D. size and shape
Step-by-step explanation:
Triangles are congruent if they have the same size and shape.
What is the length of the leg.s of the triangle below
Answers
Answer:
10
Step-by-step explanation:
Solve the equation by using the square root property.
2) (3z - 18)^2 +59 = 14
Answers
Answer:
Step-by-step explanation:
Z = i √5/3 +36
The given equation (3z - 18)^2 + 59 = 14 has no real solution because after isolating and simplifying the squared term, we would be taking the square root of a negative number, which is not possible in the real number system.
To solve the equation (3z - 18)^2 + 59 = 14 using the square root property, follow these steps:
Start by isolating the squared term:
(3z - 18)^2 = 14 - 59
Calculate the right side:
(3z - 18)^2 = -45
Since the equation involves squaring resulting in a negative number, which is not possible in the set of real numbers, this equation has no real solution.
It is important to note that squaring a real number always results in a non-negative number, so a square equal to a negative number indicates there are no real solutions to the equation.
|
Which expression is equivalent to the following complex fraction?
.
Answers
Answer:
Yes, A is correct.
Find the sum of each pair of vectors and match it with the magnitude of the resultant vector. PLEASE HELP. Information on the picture
Answers
First of all, let's write this statement in vector form. For the fist vector we have:
Magnitude 3.5 m/s, direction angle 35°:
Let's say this is vector [tex]\vec{A}[/tex], so the magnitude is:
[tex]\left|\vec{A}\right|=3.5m/s[/tex]
And the direction is defined as:
[tex]\theta = 35^{\circ}[/tex]
So the components are:
[tex]Ax=\left|\vec{A}\right| cos\theta \\ \\ Ax=3.5 cos35^{\circ}=2.86m/s \\ \\ \\ Ay=\left|\vec{A}\right| sin\theta \\ \\ Ay=3.5 sin35^{\circ}=2m/s[/tex]
So vector [tex]\vec{A}[/tex] is:
[tex]\vec{A}=2.86i+2j[/tex]
For the second vector:
Magnitude 4 m/s, direction angle 150°:
Let's say this is vector [tex]\vec{B}[/tex], so the magnitude is:
[tex]\left|\vec{B}\right|=4m/s[/tex]
And the direction is defined as:
[tex]\theta = 150^{\circ}[/tex]
So the components are:
[tex]Bx=\left|\vec{B}\right| cos\theta \\ \\ Bx=4 cos150^{\circ}=-2\sqrt{3}m/s \\ \\ \\ By=\left|\vec{B}\right| sin\theta \\ \\ By=4 sin150^{\circ}=2m/s[/tex]
So vector [tex]\vec{B}[/tex] is:
[tex]\vec{B}=-2\sqrt{3}i+2j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=\vec{A}+\vec{B}=(2.86i+2j)+(-2\sqrt{3}i+2j) \\ \\ \boxed{\vec{R}=-0.60i+4j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{Rx^2+Ry^2} \\ \\ Rx=Ax+Bx \\ \\ Ry=Ay+By \\ \\ \\ \left|\vec{R}\right|=\sqrt{(-0.6^2)+(4)^2} \\ \\ \boxed{\left|\vec{R}\right|=4.05m/s}[/tex]
2. Magnitude 4.5 m/s, direction angle 55°, magnitude 3 m/s, direction angle 135°.Matches to 5.83 m/sMagnitude 4.5 m/s, direction angle 55°:
Let's say this is vector [tex]\vec{C}[/tex], so the magnitude is:
[tex]\left|\vec{C}\right|=4.5m/s[/tex]
And the direction is defined as:
[tex]\theta = 55^{\circ}[/tex]
So the components are:
[tex]Cx=\left|\vec{C}\right| cos\theta \\ \\ Cx=4.5 cos55^{\circ}=2.58m/s \\ \\ \\ Cy=\left|\vec{C}\right| sin\theta \\ \\ Cy=4.5 sin55^{\circ}=3.68m/s[/tex]
So vector [tex]\vec{C}[/tex] is:
[tex]\vec{C}=2.58i+3.68j[/tex]
For the second vector:
Magnitude 3 m/s, direction angle 135°:
Let's say this is vector [tex]\vec{D}[/tex], so the magnitude is:
[tex]\left|\vec{D}\right|=3m/s[/tex]
And the direction is defined as:
[tex]\theta = 135^{\circ}[/tex]
So the components are:
[tex]Dx=\left|\vec{D}\right| cos\theta \\ \\ Dx=3 cos135^{\circ}=-\frac{3\sqrt{2}}{2} \\ \\ \\ Dy=\left|\vec{D}\right| sin\theta \\ \\ Dy=3 sin135^{\circ}=\frac{3\sqrt{2}}{2}[/tex]
So vector [tex]\vec{D}[/tex] is:
[tex]\vec{D}=-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=\vec{C}+\vec{D}=(2.58i+3.68j)+(-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j) \\ \\ \boxed{\vec{R}=0.46i+5.80j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(0.46)^2+(5.8)^2} \\ \\ \boxed{\left|\vec{R}\right|=5.83m/s}[/tex]
3. Magnitude 3 m/s, direction angle 70°, magnitude 3 m/s, direction angle 135°.Matches to 3.32 m/sMagnitude 4.5 m/s, direction angle 55°:
This is vector [tex]\vec{E}[/tex], so the magnitude is:
[tex]\left|\vec{E}\right|=3m/s[/tex]
Direction:
[tex]\theta = 70{\circ}[/tex]
Components:
[tex]Ex=\left|\vec{E}\right| cos\theta \\ \\ Ex=3 cos70^{\circ}=1.02m/s \\ \\ \\ Ey=\left|\vec{E}\right| sin\theta \\ \\ Ey=3 sin70^{\circ}=2.82m/s[/tex]
So:
[tex]\vec{E}=1.02i+2.82j[/tex]
For the second vector:
Magnitude 5 m/s, direction angle 210°:
[tex]\vec{F}[/tex]:
[tex]\left|\vec{F}\right|=5m/s[/tex]
Direction:
[tex]\theta = 210^{\circ}[/tex]
Components:
[tex]Fx=5 cos210^{\circ}=-\frac{5\sqrt{3}}{2} \\ \\ \\ Ey=5 sin210^{\circ}=-\frac{5}{2}[/tex]
Then:
[tex]\vec{F}=-\frac{5\sqrt{3}}{2} i-\frac{5}{2}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=(1.02i+2.82j)+(-\frac{5\sqrt{3}}{2}i-\frac{5}{2}j) \\ \\ \boxed{\vec{R}=-3.31i+0.32j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(-3.31)^2+(0.32)^2} \\ \\ \boxed{\left|\vec{R}\right|=3.32m/s}[/tex]
4. Magnitude 6 m/s, direction angle 120°, magnitude 2 m/s, direction angle 140°.Matches to 5.29 m/sMagnitude 6 m/s, direction angle 120°:
[tex]\left|\vec{W}\right|=6m/s[/tex]
Direction:
[tex]\theta = 120^{\circ}[/tex]
Components:
[tex]Wx=6 cos120^{\circ}=-3m/s \\ \\ \\ Wy=6 sin120^{\circ}=3\sqrt{3}m/s[/tex]
So:
[tex]\vec{W}=-3i+3\sqrt{3}j[/tex]
For the second vector:
Magnitude 2 m/s, direction angle 240°:
[tex]\vec{Z}[/tex]:
[tex]\left|\vec{Z}\right|=2m/s[/tex]
Direction:
[tex]\theta = 240^{\circ}[/tex]
Components:
[tex]Zx=2 cos240^{\circ}=-1 \\ \\ \\ Zy=2 sin240^{\circ}=-\sqrt{3}[/tex]
Then:
[tex]\vec{Z}=-i-\sqrt{3}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=(-3i+3\sqrt{3}j)+(-i-\sqrt{3}j) \\ \\ \boxed{\vec{R}=-4i+2\sqrt{3}j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(-4)^2+(2\sqrt{3})^2} \\ \\ \boxed{\left|\vec{R}\right|=5.29m/s}[/tex]
If f(x)=2x^2+3 and g(x)=x-2, what is (f+g)(2)?
Answers
[tex](f+g)(x)=2x^2+3+x-2=2x^2+x+1\\\\(f+g)(2)=2\cdot2^2+2+1=8+3=11[/tex]
Answer:
11
Step-by-step explanation:
(f+g)(2) means f(2)+g(2).
f(2) means we need to replace the x's in f(x)=2x^2+3 with 2.
This gives us f(2)=2(2)^2+3.
Let's simplify f(2)=2(4)+3=8+3=11.
g(2) means we need to replace the x's in g(x)=x-2 with 2.
This gives us g(2)=2-2
Let's simplify g(2)=0.
Now f(2)+g(2) means we just add the result of f(2) to the result of g(2).
So the problem is what is 11+0?
Answer is 11
The function p(x) = -2(x-9)2 + 100 used to determine the profit on T-shirts sold for x dollars. What would the profit from sales be if the price of T-shirts were 15 apiece
Answers
Answer:
$28.
Step-by-step explanation:
p(x) = -2(x - 9)^2 + 100
If the prices (x) = 15 dollars we work out the profit by substituting x = 15 in the above formula:
p(15) = -2(15 - 9)^2 + 100
= -2 * 6^2 + 100
= $28.
Answer:
28
Step-by-step explanation:
If 5+ 20 -22-3х - 10.2-2x+5, what is the value of х?
Answers
Answer:
3Step-by-step explanation:
[tex]5+20\cdot2^{2-3x}=10\cdot2^{-2x}+5\qquad\text{subtract 5 from both sides}\\\\20\cdot2^{2-3x}=10\cdot2^{-2x}\qquad\text{divide both sides by 10}\\\\2\cdot2^{2-3x}=2^{-2x}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\2^{1+2-3x}=2^{-2x}\\\\2^{3-3x}=2^{-2x}\iff3-3x=-2x\qquad\text{subteact 3 from both sides}\\\\-3x=-2x-3\qquad\tex\qquad\text{add}\ 2x\ \text{to both sides}\\\\-x=-3\qquad\text{change the signs}\\\\x=3[/tex]
5.
The letters A, L, G, E, B, R, A are on 7 tiles in a bag, one letter on each tile. If you select tiles randomly from
the bag and place them in a row from left to right, what is the probability the tiles will spell out ALGEBRA?
(Lesson 19.2) (1 point)
Answers
Answer:
1/2520
Step-by-step explanation:
First you have to find out how many different combinations can be created
7×6×5×4×3×2×1 = 5040
There is only two combinations that will spell out algebra
2/5040= 1/2520
Suppose that the time it takes to do a job is inversely proportional to the number of workers. That is, the more workers on the job the less time required to complete the job. If it takes 3 workers 16 days to finish a job, how long will it take 8 workers
Answers
Answer: 6 days.
Step-by-step explanation:
Inverse proportion equation has the form:
[tex]y=\frac{k}{x}[/tex]
Where "k" is the constant of proportionality.
Let be "y" the time it takes to do a job (number of days) and "x" the number of workers.
We can find "k" knowing that it takes 3 workers 16 days to finish a job:
[tex]16=\frac{k}{3}\\\\k=16*3\\\\k=48[/tex]
To find how long will it take 8 workers to finish the job, you must substitute the value of "k" and [tex]x=8[/tex] into [tex]y=\frac{k}{x}[/tex]. Then you get:
[tex]y=\frac{48}{8}\\\\y=6[/tex]
What are the zeros of r(p) = -p2 + 14p?
Answers
[tex]-p^2 + 14p=0\\-p(p-14)=0\\p=0 \vee p=14[/tex]
The square root of a number is between 8 and 9. Which of the following could be the value of that number? Select all that apply.
a. 8.6
b. 74
c. 80
d. 81.5
Answers
The square root of 74 is approx 8.6 and that is between 8 and 9
The square root of 80 is approx 8.9 and that is between 8 and 9
~~hope this helps~~
Final answer:
Only options b (74) and c (80) could have their square roots between 8 and 9, as their values lie between 64 (8 squared) and 81 (9 squared).
Explanation:
To find which numbers could have their square roots lying between 8 and 9, we need to consider the squares of these two numbers. 8 squared is 64 and 9 squared is 81. Therefore, any number that has a square root between 8 and 9 must be greater than 64 and less than 81.
Option a (8.6): This number is too small since its square would be much less than 64.Option b (74): This is possible because 74 lies between the squares of 8 and 9.Option c (80): This is also possible for the same reason as option b.Option d (81.5): This number cannot have a square root between 8 and 9 as it is greater than 81.Thus, the values that could be the number with the square root between 8 and 9 are 74 and 80.
Figure ABCD is a parallelogram.
What is the value of n?
Answers
Answer:
n = 17.
Step-by-step explanation:
The opposite angles of a parallelogram are congruent so we have:
4n - 2 = 2n + 32
4n - 2n = 32 + 2
2n = 34
n = 17.
The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 77 and 7. what is the length of the altitude?
Answers
Answer:
[tex]h=7\sqrt{11}\ units[/tex]
Step-by-step explanation:
The altitude to the hypotenuse of a right tringle is the geometric mean of the two segments that it divides the hypotenuse into.
1st segment = 77 units
2nd segment = 7 units
Altitude = h units
So,
[tex]h^2=77\cdot 7\\ \\h^2 =7\cdot 11\cdot 7\\ \\h=\sqrt{7\cdot 11\cdot 7}=7\sqrt{11}[/tex]
What is the product of eight factors of 10^4
Answers
Answer:
2ε + 12 [two trillion (twelve zeros)]
Step-by-step explanation:
[1][2][4][5][10][1000][2000][2500] (1 is unnecessary)
If you are talking about the FIRST 8 factors of 10000 [10⁴], then here you are. Multiply all those numbers to get the calculator notation answer above, or two trillion.
**This question is not specific enough, which was why I improvised and thought that this was what you meant. I apologize if this was not what you meant and I also hope this was what you were looking for.
I am joyous to assist you anytime.
Answer:
[tex]10^{32}[/tex].
Step-by-step explanation:
eight factors of 10^4 are
[tex]10^4*10^4*10^4*10^4*10^4*10^4*10^4*10^4 = (10^4)^8 = 10^{4*8}=10^{32}[/tex]
that is one hundred nonillion.
john is five years older than his sister. the product of their present ages is 150.
John's present age is (blank) years, and this sister's present age is (blank) years
so i believe you have to answer this with the quadratic formula but I'm not sure. please help
Answers
John's present age is 15 years, and his sister's present age is 10 years.
We have,
Let's denote John's sister's age as x.
According to the given information,
John is five years older than his sister, so John's age would be x + 5.
The product of their present ages is 150, which means:
x * (x + 5) = 150
Expanding the equation:
x² + 5x = 150
Rearranging the equation to standard quadratic form:
x² + 5x - 150 = 0
Now we can solve this quadratic equation.
Factoring or using the quadratic formula will give us the values of x, representing the sister's age.
Factoring the equation:
(x - 10)(x + 15) = 0
Setting each factor to zero:
x - 10 = 0 or x + 15 = 0
Solving for x:
x = 10 or x = -15
Since ages cannot be negative, we can discard the solution x = -15. Therefore, the sister's present age is x = 10.
John's present age is then calculated by adding 5 years to his sister's age:
John's age = x + 5 = 10 + 5 = 15 years.
Thus,
John's present age is 15 years, and his sister's present age is 10 years.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
By forming a quadratic equation from the given problem, we determine that John's present age is 15 years and his sister's present age is 10 years.
Let's designate John's age as J and his sister's age as S. We've been given two pieces of information: John is five years older than his sister, and the product of their present ages is 150. Mathematically, these can be expressed as:
J = S + 5J * S = 150Substituting the first equation into the second gives us:
(S + 5) * S = 150
Expanding and rearranging, we get a quadratic equation:
S2 + 5S - 150 = 0
To solve for S, we can either factor the quadratic equation or use the quadratic formula. Factoring seems simpler in this case:
(S + 15)(S - 10) = 0
This gives us two possible values for S: -15 and 10. Since ages cannot be negative, we discard S = -15 and keep S = 10. Now we can find John's age:
J = S + 5 = 10 + 5 = 15
Therefore, John's present age is 15 years, and his sister's present age is 10 years.
This graph represents the function f(x) = x^2 - 4x + 3/ x^2 + ax + b. a= ___ b= ___
Answers
Answer:
f(x) = (x+2)(x-8)/(x-6)(x+4) <-> x=6,x=-4
i(x) = (x-4)(x-6)/(x-2)(x+8) <-> x=2,x=-8
k(x) = (x-2)(x+8)/(x+6)(x-4) <-> x=-6,x=4
m(x) = (x+4)(x-6)/(x+2)(x-8) <-> x=-2,x=8
Step-by-step explanation:
The function is discontinuous if the denominator is zero.
We will check for which function the values are given
1) f(x) = (x+2)(x-8)/(x-6)(x+4)
if x = 6 and x = -4 the denominator is zero
So, x=6 and x=-4 given
2) g(x) = (x+4)(x-8)/(x+2)(x-6)
if x = -2 and x = 6 the denominator is zero
So, x= -2 and x= 6 not given so, g(x) will not be considered
3) h(x)= (x+2)(x-6)/(x-8)(x+4)
if x = 8 and x = -4 the denominator is zero
So, x= 8 and x= -4 not given so, h(x) will not be considered
4) i(x) = (x-4)(x-6)/(x-2)(x+8)
if x = 2 and x = -8 the denominator is zero
So, x= 2 and x= -8 given
5) j(x) = (x-2)(x+6)/(x-4)(x+8)
if x = 4 and x = -8 the denominator is zero
So, x= 4 and x= -8 not given so, j(x) will not be considered
6) k(x) = (x-2)(x+8)/(x+6)(x-4)
if x = -6 and x = 4 the denominator is zero
So, x= -6 and x= 4 given
7) l(x) = (x-4)(x+8)/(x+6)(x-2)
if x = -6 and x = 2 the denominator is zero
So, x= -6 and x= 2 not given so, l(x) will not be considered
8) m(x) = (x+4)(x-6)/(x+2)(x-8)
if x = -2 and x = 8 the denominator is zero
So, x= -2 and x= 8 given
. Solve the triangle. A = 32°, a = 19, b = 12 B = 19.6°, C = 148.4°, c ≈22.5 B = 19.6°, C = 128.4°, c ≈28.1 Cannot be solved B = 19.6°, C = 128.4°, c ≈16.9
Answers
Answer:
Step-by-step explanation:
sin(32)/19 = sin(B)/12
cross multiply
12 sin(32) = 19 sin(B)
sin(B) = 12 sin(32) /19 = 0.334686
B = sin°-1(0.334686)
B = 0.321272 radian
B = (0.321272)*180/pi degrees = 19.55°
C = 180-32-19.55 = 128.45°
sin(32)/19 = sin(128.45)/ c
cross multiply
c sin(32) = 19 sin(128.45)
c = 19 sin(128.45) /sin(32) =28.08....
y= 3x2 + 6x + 1
What’s the answer
Answers
Answer
Y= 3 × 2 + 6x + 1 = 6 + 6x +1 = 6x + (6+1) = 6x + 7
Answer:
This is a function, so the answer is a plot, you can see it in the attached picture
Step-by-step explanation:
This is a function, the best way to go here is to graph.
First lest find the roots of 3x2+6x+1, you do this by using the quadratic equation
[tex]x_{1} = \frac{-b + \sqrt{b^{2}-4ac }}{2a}\\x_{2} = \frac{-b - \sqrt{b^{2}-4ac }}{2a}[/tex]
Where a=3, b=6, c=1
Using that, you get, x1 = -1 - sqrt(2/3) which is a negative number, and x2=sqrt(2/3) - 1 which is a negative number.
These number represent values that makes the function equals =0
Now if we make x=0, the result is y=1,
We have a better idea of what is to plot and it is shown on the attached picture
Write the product in its simplest form
-3y.3y4
Enter the correct answer.
Answers
Answer:
[tex]\large\boxed{-9y^5}[/tex]
Step-by-step explanation:
[tex]-3y\cdot3y^4=(-3\cdot3)(y\cdot y^4)\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=-9y^{1+4}=-9y^5[/tex]
Marcos purchases a top-up card for his pre-paid cell phone. His remaining balance, B, can be modeled by the equation B=40−0.1n, where n is the number of minutes he's talked since purchasing the card.
a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?
b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?
c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?
Answers
Answer:
Part a) When Marcos purchased the card, the balance on the card was $40
This is the B-intercept
Part b) Mark will have spoken 400 minutes when he runs out of money
This is the n-intercept
part c) The slope of the equation is -0.1 and the units are dollars per minute
Step-by-step explanation:
we have
[tex]B=40-0.1n[/tex]
where
B is balance in dollars on the card
n is the number of minutes
Part a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?
we know that
The B-intercept is the value of B when the value of n is equal to zero
so
For n=0
substitute and find the value of B
[tex]B=40-0.1(0)=\$40[/tex]
therefore
When Marcos purchased the card, the balance on the card was $40
This is the B-intercept
Part b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?
we know that
The n-intercept is the value of n when the value of B is equal to zero
so
For B=0
substitute and find the value of n
[tex]0=40-0.1n[/tex]
[tex]0.1n=40[/tex]
[tex]n=400\ minutes[/tex]
therefore
Mark will have spoken 400 minutes when he runs out of money
This is the n-intercept
Part c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?
we have
[tex]B=40-0.1n[/tex]
This is is the equation of the line into slope intercept form
[tex]m=-0.1\frac{\$}{minute}[/tex] -----> slope of the equation
[tex]b=40[/tex] ------> the B-intercept
The units of the slope are dollars per minute
Marcos purchased a top-up card with an initial balance of $40 (B-intercept). He will run out of money after 400 minutes of call time (n-intercept). The charge rate is $0.1 per minute (slope).
Explanation:a) The money on the card when he purchased it is given by the constant term in the equation, which is $40. This is the B-intercept, because it is the value of B when n = 0 (meaning no minutes have been used).
b) Marcos will have run out of money when B = 0. To find this, set B = 0 and solve for n: 0 = 40 - 0.1n, which leads to n = 400. So, Marcos will have talked for 400 minutes when he runs out of money. This is the n-intercept. It represents the value of n when B = 0 (meaning there is no money left on the card).
c) The slope of this equation is -0.1. In the context of this problem, the slope represents the rate at which money is deducted from the balance for each minute of talk time. Therefore, the units on the slope are dollars per minute.
Learn more about Linear equation here:https://brainly.com/question/32634451
#SPJ3
Find the quadratic function that fits the following data. which one function fits.
Answers
Answer:
C
Step-by-step explanation:
The general rule for the quadratic function is
[tex]y=ax^2+bx+c[/tex]
Use the data from the table:
[tex]y(50)=130\Rightarrow 130=a\cdot 50^2+b\cdot 50+c\\ \\y(70)=130\Rightarrow 130=a\cdot 70^2+b\cdot 70+c\\ \\y(90)=200\Rightarrow 200=a\cdot 90^2+b\cdot 90+c[/tex]
We get the system of three equations:
[tex]\left\{\begin{array}{l}2500a+50b+c=130\\ \\4900a+70b+c=130\\ \\8100a+90b+c=200\end{array}\right.[/tex]
Subtract these equations:
[tex]\left\{\begin{array}{l}4900a+70b+c-2500a-50b-c=130-130\\ \\8100a+90b+c-2500a-50b-c=200-130\end{array}\right.\Rightarrow \left\{\begin{array}{l}2400a+20b=0\\ \\5600a+40b=70\end{array}\right.[/tex]
From the first equation
[tex]b=-120a[/tex]
Substitute it into the second equation:
[tex]5600a+40\cdot (-120a)=70\Rightarrow 800a=70,\\ \\ a=\dfrac{7}{80},\\ \\ b=-120\cdot \dfrac{7}{80}=-\dfrac{21}{2}=-10.5[/tex]
So,
[tex]2500\cdot \dfrac{7}{80}+50\cdot (-10.5)+c=130\Rightarrow 218.75-525+c=130\\ \\c=130-218.75+525=436.25[/tex]
The quadratic function is
[tex]y=\dfrac{7}{80}x^2-10.5x+436.25\\ \\y=0.0875x^2-10.5x+436.25[/tex]
How would u solve this problem ?
Answers
Answer:
9×80=x×15
x=58lbs
Step-by-step explanation:
Considering no frictions applyd, the value of the report of the two forces ( F- the action force and R- the resistance force) equals the value of the report between the value of the distance from the folcrum to the rock and the value of the distance from the fulcrum to the active force
A rectangle has vertices at (-1,6), (-1,-2), (3,6), and (3,-2). Sara says the area of the rectangle is 16 square units and her
work is shown below
Steps
Step 1
Step 2
Step 3
Sara's Work
Base: 113-4
Height: 161+F2-4
Area: 4x4-16 square units
Where, if at all, did Sara first make a mistake in finding the area of the rectangle?
Step 1
Step 2
Step 3
no mistake
Answers
Answer:
Step 2
Step-by-step explanation:
Let
[tex]A(-1,6), B(-1,-2), C(3,6), D(3,-2)[/tex]
Plot the vertices to better understand the problem
see the attached figure
The area of the rectangle is equal to
[tex]A=bh[/tex]
we have
[tex]b=BD\\ h=BA[/tex]
step 1
Find the base b (BD)
[tex] B(-1,-2),D(3,-2)[/tex]
[tex]b=\left|3\right|+\left|-1\right|=4\ units[/tex]
step 1 is correct
step 2
Find the height h (BA)
[tex]B(-1,-2),A(-1,6)[/tex]
[tex]h=\left|6\right|+\left|-2\right|=8\ units[/tex]
step 2 is not correct
step 3
Find the area
[tex]A=(4)(8)=32\ units^{2}[/tex]
Therefore
Sara first make a mistake in finding the area of the rectangle in Step 2
Answer:
step 2
Step-by-step explanation:
A cylinder has a radius of 6 inches and is 15 inches tall. What is the approximate volume of the cylinder? Express the answer in terms of pi.
Answers
Answer:
The volume of cylinder = 540π inches²
Step-by-step explanation:
Points to remember
Volume of cylinder = πr²h
Where r - Radius of cylinder and
h - Height of cylinder
To find the volume of cylinder
Here r = 6 inches and height h = 15 inches
Volume = πr²h
= π * 6² * 15
= π * 36 * 15
= 540 πinches²
The volume of cylinder = 540π inches²
where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?
Answers
Answer:
The circumference is a irrational number
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
In this problem we have that
[tex]D=d\ units[/tex] ---> is a rational number
substitute
[tex]C=\pi (d)[/tex]
[tex]C=d\pi\ units[/tex]
Remember that
The number π is a irrational number
and
If you multiply a rational number by a irrational number, the result is a irrational number
therefore
The circumference is a irrational number
A factory manufactures widgets based on customer orders. If a customer's order is for less than w widgets, the customer's cost per widget is d dollars. If a customer's order is for at least w widgets, the customer's cost per widget is decreased by c cents for each widget ordered over w widgets. A customer's total cost is t. Which of the following functions would best model the situation given above?
Answers
Answer:
Piecewise function model
Step-by-step explanation:
According to the given statement a factory manufactures widgets based on customer orders. If a customer's order is for less than w widgets, the customer's cost per widget is d dollars.
customer order < widgets
If a customer's order is for at least w widgets, the customer's cost per widget is decreased by c cents for each widget ordered over w widgets. A customer's total cost is t.
customer order > widgets
We can notice that we have two different conditions. In this type of question where there are different conditions for different types of domain we use piecewise function.
With different conditions, the cost is different, therefore piecewise function model would be the best option for the situation....
Which is the graph of f(x) =4(1/2)^x
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=4(\frac{1}{2})^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
r is the rate
b=1+r
In this problem we have
a=4 ----> initial value (y-intercept)
b=1/2
so
1+r=1/2
r=1/2-1=-1/2
r=-0.5=-50% ----> is negative because is a decrease rate
using a graphing tool
The graph in the attached figure